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Abstract:

A laser cavity includes a gain medium for amplifying a light pulse in a
light path, wherein the gain medium has a gain profile for amplifying the
light pulse as a function of wavelength; at least one mirror on one side
of the gain medium; and an output coupler. The output coupler has an
output coupling profile for inducing loss in the light pulse as a
function of wavelength that substantially matches the saturated gain
profile of the gain medium across a range of lasing wavelengths. The
purpose of this device is to achieve a flattened net-gain profile to
substantially improve mode-locking performance with respect to
self-starting, beam-quality, and broadband operation.

Claims:

1. A laser cavity comprising: a gain medium for amplifying a light pulse,
the gain medium having a saturated gain profile for amplifying the light
pulse as a function of wavelength; at least one mirror on one side of the
gain medium; and an output coupler that, together with the mirror(s),
defines a light path in the laser cavity, wherein the gain medium is
positioned in the light path and the output coupler has a output coupling
profile for inducing loss in the light pulse as a function of wavelength,
wherein the output coupling profile of the output coupler substantially
matches the saturated gain profile of the gain medium across a range of
lasing wavelengths.

2. The laser cavity of claim 1, wherein the range of wavelengths over
which the output coupling profile of the output coupler substantially
matches the saturated gain profile of the gain medium extends across at
least 25% of the full-width-half-maximum of the saturated gain profile.

3. The laser cavity of claim 1, wherein the range of wavelengths over
which the output coupling profile of the output coupler substantially
matches the saturated gain profile of the gain medium extends across at
least 50% of the full-width-half-maximum of the saturated gain profile.

4. The laser cavity of claim 1, wherein the range of wavelengths over
which the output coupling profile of the output coupler substantially
matches the saturated gain profile of the gain medium extends across at
least 100% of the full-width-half-maximum of the saturated gain profile.

5. The laser cavity of claim 1, wherein the range of wavelengths over
which the output coupling profile of the output coupler substantially
matches the saturated gain profile of the gain medium extends across at
least 200% or more of the full-width-half-maximum of the saturated gain
profile.

6. The laser cavity of claim 1, wherein the output coupler includes a
substrate and a dielectric coating, wherein the output coupling profile
is due to the dielectric coating.

7. The laser cavity of claim 6, wherein the dielectric coating comprises
alternating layers of a lower-refractive-index material and a
higher-refractive index material.

8. The laser cavity of claim 7, wherein the lower-refractive-index
material is SiO2 and the higher-refractive index material is
selected from Nb2O5, TiO2 and Ta2O.sub.5.

15. A method for constructing a short pulse laser comprising: circulating
a light pulse within a closed optical path in a laser cavity; repeatedly
passing the light pulse through a gain medium in the cavity, wherein the
gain medium amplifies the light pulse with a saturated gain profile as a
function of lasing wavelengths; and directing all or part of the light
pulse from the cavity with an output coupler, wherein the output coupler
induces a loss profile on the light pulse that substantially matches the
saturated gain profile across a range of the lasing wavelengths.

16. The method of claim 15, wherein the range of wavelengths over which
the loss profile of the output coupler substantially matches the
saturated gain profile of the gain medium extends across at least 25% of
the full-width-half-maximum of the laser gain profile.

17. The method of claim 15, wherein the output coupler partially removes
the light pulse from the cavity by reflecting the light pulse.

18. The method of claim 15, wherein the output coupler wherein the output
coupler partially removes the light pulse from the cavity by transmitting
the light pulse.

Description:

RELATED APPLICATION

[0001] This application claims the benefit of U.S. Provisional Application
No. 61/325,434, filed Apr. 19, 2010, the entire content of which is
incorporated herein by reference.

BACKGROUND

[0003] Mode-locking using Kerr nonlinearity, also known as Kerr-lens
mode-locking (KLM), can be used to generate ultrashort pulses in the
few-cycle regime directly from laser oscillators. The KLM mechanism,
which is an effective saturable absorber, leads to pulse shortening; and
the pulse shortening counters pulse lengthening that is caused by gain
filtering experienced by the pulses. Consequently, mode-locked lasers
generating femtosecond pulses are pumped well above the threshold for
obtaining enough intracavity pulse energy to induce the nonlinearity and
are operated on one of the edges of the cavity stability regions where
the KLM strength is maximized, which usually results in less-stable
operation, critical cavity alignment and reduced beam quality.

[0004] If, however, there would be no or only strongly reduced gain
filtering, which implies that the total cavity loss has the same spectral
profile as the gain, an arbitrary low KLM action could sustain short
pulses covering the spectral range where the intracavity dispersion is
well compensated. This result may lead to mode-locking with less cavity
misalignment, lower intracavity pulse energy, and greatly improved beam
quality. Creation of such frequency-dependent intracavity loss has been
demonstrated previously by adding a thin angle-tuned etalon in a
titanium-doped sapphire (Ti:sapphire) regenerative amplifier [C. P. J.
Barty, et al., "Regenerative Pulse Shaping and Amplification of
Ultrabroadband Optical Pulses,"0 21 Opt. Lett. 219-221 (1996)]. There are
several disadvantages, however, of using etalons in laser oscillators,
including the following:

[0005] (1) the etalon behaves as an additional lossy component that
dramatically lowers the laser efficiency;

[0006] (2) since etalons are based on multiple reflections between two
fixed surfaces, the shape of the transmittivity and transmitted phase are
dominated by the interference behavior and cannot be controlled
independently; and

[0007] (3) for broadband lasers, the thickness of the required etalon will
be very small, which makes it very challenging, in terms of alignment and
manufacturing capabilities, to produce loss with the right peak location
and linewidth.

SUMMARY

[0008] Mode-locked laser cavities with gain-matching output couplers and
methods for using the laser are described herein. Various embodiments of
the apparatus and methods may include some or all of the elements,
features and steps described below.

[0009] The laser cavity can include a gain medium for amplifying a light
pulse, wherein the gain medium has a gain profile for amplifying the
light pulse as a function of wavelength across a range of wavelengths; at
least one mirror on one side of the gain medium; and an output coupler
that, together with the mirror(s), defines a light path in the laser
cavity. The gain medium is positioned in the light path, and the output
coupler has a loss profile for coupling out the light pulse as a function
of wavelength across the range of wavelengths. The loss profile of the
output coupler substantially matches the gain profile of the gain medium
across the range of wavelengths (e.g., wherein the saturated gain and
loss profiles, when normalized to its own peak value, diverge from each
other by less than a value of 1%, 3%, 5%, 10% or 20% across the range of
wavelengths).

[0010] The output couplers of this invention can be used to introduce loss
that closely matches the gain profile in the cavity without dramatically
affecting laser efficiency while still maintaining well-compensated
intracavity dispersion over the entire gain bandwidth. The output
couplers can accordingly provide for more-stable laser operation, can
increase the ease by which amplified pulses are obtained in the laser
cavity, and can reduce the power needed (e.g., down to the level just
above the lasing threshold , which is 2.5 W in our demonstration) to
obtain a short amplified pulse in the laser cavity

BRIEF DESCRIPTION OF THE DRAWINGS

[0011]FIG. 1 is a schematic illustration of a linear cavity with a
gain-matching transmitting output coupler.

[0012] FIG. 2 is a schematic illustration of a linear cavity with a
gain-matching reflecting output coupler.

[0013] FIG. 3 is a schematic illustration of a ring cavity with a
gain-matching transmitting output coupler.

[0014]FIG. 4 is a schematic illustration of a ring cavity with a
gain-matching reflecting output coupler.

[0015]FIG. 5 is a plot of a cavity gain and loss profile in
continuous-wave operation where the gain is provided by the laser medium
only as a function of frequency against a constant loss, supporting a
single lasing frequency or a narrow band of lasing frequencies.

[0016] FIG. 6 is a plot of a cavity gain and loss profile in conventional
nonlinearity-assisted mode-locking operation with low pulse energy where
the gain as a function of frequency is assisted by a weak Kerr-lens
effect against a constant loss, supporting pulses with broader bandwidth.

[0017] FIG. 7 is a plot of a cavity gain and loss profile in conventional
nonlinearity-assisted mode-locking operation with high pulse energy where
the gain as a function of frequency is assisted by a strong Kerr-lens
effect against a constant loss, supporting pulses with even broader
bandwidth.

[0018] FIG. 8 is a plot illustrating how mode-locking assisted by
Kerr-lens nonlinearity starts in a laser cavity from perturbations.

[0019] FIG. 9 is a plot of a cavity gain and loss profile in the
mode-locking operation requiring much reduced nonlinearity where the
laser loss as a function of frequency matches the laser gain profile as a
function of frequency due to the introduction of a gain-matching output
coupler.

[0020]FIG. 10 is a schematic illustration of a Ti:sapphire laser
configuration for experimental demonstration.

[0021] FIG. 11 shows the output beam profile from the laser configuration
of FIG. 10 after passing through a 10-nm interference filter centered at
570 nm.

[0022] FIG. 12 shows the output beam profile from the laser configuration
of FIG. 10 after passing through a 10-nm interference filter centered at
900 nm.

[0023] FIG. 13 shows the output beam profile from the laser configuration
of FIG. 10 after passing through a 10-nm interference filter centered at
1140 nm.

[0024] FIG. 14 shows the output beam profile from the laser configuration
of FIG. 10 with no filter.

[0025] FIG. 15 is a plot of pump power versus laser output power in
mode-locked and continuous-wave operation (left axis) and intracavity and
output pulsewidth (right axis).

[0026]FIG. 16 provides a series of plots of intracavity spectra under
different pump power levels.

[0027] FIG. 17 is a plot of transmission, group delay and gain profile as
a function of wavelength.

[0029] In the accompanying drawings, like reference characters refer to
the same or similar parts throughout the different views. The drawings
are not necessarily to scale, emphasis instead being placed upon
illustrating particular principles, discussed below.

DETAILED DESCRIPTION

[0030] The foregoing and other features and advantages of various aspects
of the invention(s) will be apparent from the following, more-particular
description of various concepts and specific embodiments within the
broader bounds of the invention(s). Various aspects of the subject matter
introduced above and discussed in greater detail below may be implemented
in any of numerous ways, as the subject matter is not limited to any
particular manner of implementation. Examples of specific implementations
and applications are provided primarily for illustrative purposes.

[0031] Unless otherwise defined, used or characterized herein, terms that
are used herein (including technical and scientific terms) are to be
interpreted as having a meaning that is consistent with their accepted
meaning in the context of the relevant art and are not to be interpreted
in an idealized or overly formal sense unless expressly so defined
herein. For example, if a particular composition is referenced, the
composition may be substantially, though not perfectly pure, as practical
and imperfect realities may apply; e.g., the potential presence of at
least trace impurities (e.g., at less than 1 or 2% by weight or volume)
can be understood as being within the scope of the description; likewise,
if a particular shape is referenced, the shape is intended to include
imperfect variations from ideal shapes, e.g., due to machining
tolerances.

[0032] Although the terms, first, second, third, etc., may be used herein
to describe various elements, these elements are not to be limited by
these terms. These terms are simply used to distinguish one element from
another. Thus, a first element, discussed below, could be termed a second
element without departing from the teachings of the exemplary
embodiments.

[0033] Spatially relative terms, such as "above," "upper," "beneath,"
"below," "lower," and the like, may be used herein for ease of
description to describe the relationship of one element to another
element, as illustrated in the figures. It will be understood that the
spatially relative terms, as well as the illustrated configurations, are
intended to encompass different orientations of the apparatus in use or
operation in addition to the orientations described herein and depicted
in the figures. For example, if the apparatus in the figures is turned
over, elements described as "below" or "beneath" other elements or
features would then be oriented "above" the other elements or features.
Thus, the exemplary term, "above," may encompass both an orientation of
above and below. The apparatus may be otherwise oriented (e.g., rotated
90 degrees or at other orientations) and the spatially relative
descriptors used herein interpreted accordingly.

[0034] Further still, in this disclosure, when an element is referred to
as being "on," "connected to" or "coupled to" another element, it may be
directly on, connected or coupled to the other element or intervening
elements may be present unless otherwise specified.

[0035] The terminology used herein is for the purpose of describing
particular embodiments and is not intended to be limiting of exemplary
embodiments. As used herein, the singular forms, "a," "an" and "the," are
intended to include the plural forms as well, unless the context clearly
indicates otherwise. Additionally, the terms, "includes," "including,"
"comprises" and "comprising," specify the presence of the stated elements
or steps but do not preclude the presence or addition of one or more
other elements or steps.

[0036] Described herein is a laser output coupler (OC), called
"gain-matched OC," that incorporates into its output-coupling profile a
frequency-dependence that has the same (or substantially the same)
spectral profile as the gain to reduce the gain-filtering effect. In the
absence of an additional lossy component introduced to the cavity, the
laser efficiency will not be negatively affected. Within the gain
bandwidth of the laser gain medium, the main features of the output
coupler are as follows:

[0037] (1) the output coupling is designed to have the same spectral
profile in terms of shape, bandwidth, and peak locations as the gain
spectrum of the laser gain medium; and

[0038] (2) the dispersion added to the circulating intracavity pulses by
the output coupler can be compensated using low loss components (e.g.,
chirped mirrors, materials at Brewster's angle, etc.).

[0039] In practice, the above features can be implemented on the
dielectric coating on the reflecting or transmitting output couplers used
in both linear and ring cavity lasers. As used herein, a "transmitting
output coupler" is a component used to transmit part of the circulating
intracavity optical power as laser output, while a "reflecting output
coupler" is a component used to reflect part of the circulating
intracavity optical power as laser output.

[0040] Representative configurations of the inverse-gain/gain-matched
output couplers are shown in FIGS. 1-4. A linear cavity laser 12 with a
transmitting output coupler 22 is shown in FIG. 1. The linear cavity is
bounded with a laser mirror 24, with the intracavity pulse 26 circulating
(e.g., reciprocating) through a gain medium 28 there between and an
output pulse 30 exiting through the transmitting output coupler 22. A
linear cavity laser 12 with a reflecting output coupler 32 is shown in
FIG. 2. In this embodiment, the linear cavity is bounded with a pair of
laser mirrors 24, and the gain medium 28 and the reflecting output
coupler 32 are positioned between the mirrors 24 in the path of the
reciprocating intracavity pulse 26. The output pulse 30 is reflected out
of the cavity by the reflecting output coupler 32. The gain medium 28 can
comprise, for example, titanium-doped sapphire (Ti:Sapphire),
chromium-doped forsterite (Cr:Mg2SiO4), Cr4+:YAG, Yb-doped
lasers, Er-doped lasers, Er:Yb-doped lasers, Tm-doped lasers, Ho-doped
lasers, ZnSe, chromium-doped LiCaAlF6 (Cr:LiCAF), and chromium-doped
LiSrAlF6 (Cr:LiSAF). The output coupler 32 can comprise, for
example, alternating layers of (a) a low-refractive-index material, such
as SiO2, and (b) a high-refractive index material, such as
Nb2O5, TiO2 or Ta2O5.

[0041] A ring cavity laser 12 with a transmitting output coupler 22 is
shown in FIG. 3, wherein the intracavity pulse 26 traverses a ring cavity
bounded by the transmitting output coupler 22 and two laser mirrors 24.
The gain medium 28 is positioned in one branch of the ring, and the
output pulse 30 exits through the transmitting output coupler 22. A ring
cavity laser 12 with a reflecting output coupler 32 is shown in FIG. 4.
In this embodiment, the ring cavity is bounded by three laser mirrors 24,
and the output pulse 30 is reflected out of the ring cavity by the
reflecting output coupler 32.

[0042] The cavities illustrated in FIGS. 1-4 can be waveguide-based, in
free-space, or a mix of the two. The intracavity pulses 26 can therefore
be guided by the laser mirrors 24, as shown in the schematic
illustrations of FIGS. 1-4, or by any of various types of waveguide,
which enables the omission of some of the illustrated laser mirrors 24.
However, one can also use more laser mirrors 24 to fold the laser cavity.
The gain medium 28 can be a free-space component or a section of doped
waveguide. The transmitting output coupler 22 is designed with a
transmission that matches the gain spectrum; and the reflected phase that
is added to the circulating intracavity pulse 26 can be well-controlled
within the bandwidth of the gain medium 28. In the design of reflecting
output couplers 33, the output coupler 32 is designed with a reflectivity
that matches the gain spectrum; and the transmitted phase that is added
to the circulating intracavity pulse 26 can be well-controlled within the
bandwidth of the gain medium 28.

[0043] The process by which a laser with a constant loss profile changes
from continuous-wave operation (FIG. 5) to mode-locking operation with
the aid of nonlinearity of different strengths is illustrated via the
plots of FIGS. 6 and 7. In continuous-wave operation, the laser with
constant loss 42 has a gain profile as a function of frequency 40 that is
solely provided by the gain medium, wherein only a single frequency or a
narrow band of frequencies lase due to a strong gain-filtering effect.
With small perturbations to the cavity, more neighboring modes will be
emitted for a short time period, which generates instantaneous optical
pulses inside the cavity that help to initiate mode-locking through the
Kerr-nonlinearity. The Kerr-nonlinearity provides additional gain
proportional to the pulse intensity by affecting the beam overlap with
the gain medium that favors high-intensity pulses. This extra gain
assists to compensate for the gain-filtering effect that hampers the
mode-locking operation. The effects of weak and strong Kerr-lens assisted
gain are shown in FIG. 6 and FIG. 7, respectively. The broadened
effective gain profiles 44 caused by the Kerr-lens nonlinearity of
different strengths support pulses of different bandwidths as shown. To
overcome strong gain-filtering, larger intracavity pulse energy is
required for initiation of mode-locking and to support ultrashort pulses.

[0044] An illustration of how mode-locking assisted by Kerr-lens
nonlinearity starts in a laser cavity from perturbations is provided in
FIG. 8. Due to the Kerr-lens nonlinearity, pulses with different
intensity see different overlap with the pump beam and get different
amplification accordingly. When the cavity is perturbed, a few
frequencies lase simultaneously and produce random intracavity pulses
with high instantaneous intensity. When the cavity is aligned in such a
way that benefits a high intensity, a stronger pulse can collect more
photons than weaker ones after each round-trip and becomes even stronger.
After several round-trips, only the strongest pulse survives.

[0045] FIG. 9 illustrates the flattening of the net-gain profile by
incorporating into the laser cavity a gain-matched output coupler having
an output coupling profile 46 as a function of frequency that
approximately matches the profile of the gain 40. The gain-filtering
effect is greatly reduced, even eliminated, or even overcompensated due
to the output coupler, which consequently lowers the required intracavity
pulse energy for initiation of mode-locking and broadband operation.

Experimental Demonstration of the Invention:

[0046] For this experimental demonstration, a broadband dielectric
transmitting output coupler was designed for linear-cavity Ti:sapphire
lasers. With this output coupler, mode-locking was initiated and run
stably with pump powers just above the continuous wave (cw) lasing
threshold. In order to design the output coupler with a loss profile that
matched the gain profile, the gain profile of Ti:sapphire crystal was
first measured and used to optimize a dielectric output coupler coating
with a peak transmission of 4% using 47 layers of
SiO2/Nb2O5 on a fused-silica substrate. As shown in FIGS.
10-14, the corresponding dispersion of the output coupler 22 can be
compensated with a 1.1 mm-thick BaF2 plate 50 placed at the Brewster
angle.

[0048] No significant changes in mode size were observed when changing the
pump power. The laser can be initiated very easily by slightly tapping
the end mirror. Compared to the original laser with an uncompensated
gain-filtering effect, the new design, described herein, can provide the
following advantages:

[0049] (1) much better beam quality with nearly no wavelength dependence
across the octave-spanning range,

[0050] (2) stronger resistance to environmental disturbances even when the
cavity is directly exposed to free space,

[0051] (3) a much lower mode-locking threshold, and

[0052] (4) an ability to operate the cavity in the center of the stability
range; the laser, therefore, is more stable in response to perturbations.

[0053] To quantitatively evaluate the performance of the laser, several
laser parameters for different pump power levels were measured and
plotted in FIG. 15, which shows the continuous-wave power 60, the
mode-locked power 62, the output pulsewidth 64, and the intracavity
pulsewidth 66. The intracavity spectra under different pump powers are
shown in FIG. 16. The results include the following.

[0054] (1) Mode-locking was initiated at 2.9-W continuous-wave pump power
(shown by plot 60), which is just above the continuous wave threshold of
2.85 W, when the continuous wave output power was only 7 mW.

[0055] (2) Once mode-locked, the mode-locked pump power (shown by plot 62)
could be further decreased to 2.5 W while still generating a
transform-limited output pulsewidth (τ) 44 of less than 8 fs with
greater than 100-mW output power.

[0056] (3) Due to the special profile of the inverse-gain output coupler,
the average cavity loss due to output coupling decreased as the laser
bandwidth increased. This relationship explains the large difference
between the continuous-wave output power 60 and the mode-locked output
power 62 near the laser threshold. The output pulsewidths (τ) 64 were
longer than the intracavity pulsewidths (τ) 66.

[0057] (4) As pump power increased, the intracavity pulse energy also
increased, which induced more nonlinearity and consequently resulted in
more broadband spectra and shorter pulsewidths (τ). However, the
output power stayed almost constant since the increase in intracavity
pulse energy was compensated by the decrease in output coupling.

[0058] The method was demonstrated here towards using the required
nonlinearity in a modelocked laser using the Kerr-Lens-Mode-locking
technique. However, the method is in general applicable to any modelocked
laser to reduce the required nonlinearity.

[0059] In FIG. 17, the gain profile 70 of a titanium:sapphire gain medium
in a laser cavity and the transmission profile 72 of a gain-matched
output coupler through which the pulse exits the cavity are plotted as a
function of wavelength. As shown, the gain profile 70 of the gain medium
and the transmission profile 72 of the output coupler approximately match
over a substantial band of wavelengths. The group delay 74 of the pulse
is also plotted as a function of wavelength in FIG. 17. The wavelength
range of the output laser pulse is about 600 nm to about 1000 nm.

[0060] The output coupler used in the system for which the profiles are
plotted in FIG. 17 comprises 47 layers of alternating SiO2 and
Nb2O5 stacks. A plot showing the layer-by-layer thickness
profile of a SiO2/Nb2O5 gain-matched output coupler is
provided in FIG. 18, wherein the odd-numbered layers represent SiO2,
and the even-numbered layers represent Nb2O5. Dispersion of the
output coupler in this embodiment can be compensated by a 1.1 mm
BaF2 plate.

[0061] Variables of the output coupler that can be manipulated to match
the profile of the gain medium include composition (to thereby manipulate
the refractive index through the output coupler), the number of layers in
the output coupler, and the thickness of each layer. As shown for the
embodiment of FIG. 18, the layers of the output coupler can include an
alternating sequence of (a) a low-refractive-index material, such as
SiO2, and (b) a high-refractive index material, such as
Nb2O5, TiO2 or Ta2O5.

[0062] The design of the layered structure of the output coupler can be
carried out using a computer including a processor coupled with a
computer-readable storage medium in which is stored an optical-coating
design tool, such as OPTILAYER thin-film software (available from
OptiLayer, Ltd., Moscow, Russia). One can start with an initial base
configuration of layers and then, in an iterative process, determine via
a global algorithm where the greatest impact toward matching the profile
of the gain medium can be made by (1) increasing or decreasing the layer
thickness of one or more of the layers, (2) adding or removing one or
more layers from the structure, or (3) changing the type of material
assigned to one or more layers until a structure is generated (such as a
structure having the design shown in FIG. 18) that will have an output
coupling profile (the output coupling can be considered as loss for the
laser cavity) substantially matching that of the gain medium. Moreover,
the dispersion added to the circulating intracavity pulses due to the
output-coupler design can be compensated by other types of low-loss
components (e.g., chirped mirrors, materials at Brewster's angle, etc.).
The design tool(s) perform iterative procedures that optimize towards
minimum weighted deviation from the design goal of output coupling and
dispersion based on the concept mentioned above.

[0063] In describing embodiments of the invention, specific terminology is
used for the sake of clarity. For the purpose of description, specific
terms are intended to at least include technical and functional
equivalents that operate in a similar manner to accomplish a similar
result. Additionally, in some instances where a particular embodiment of
the invention includes a plurality of system elements or method steps,
those elements or steps may be replaced with a single element or step;
likewise, a single element or step may be replaced with a plurality of
elements or steps that serve the same purpose. Further, where parameters
for various properties are specified herein for embodiments of the
invention, those parameters can be adjusted up or down by 1/100th,
1/50th, 1/20th, 1/10th, 1/5th, 1/3rd, 1/2,
3/4th, etc. (or up by a factor of 2, 5, 10, etc.), or by rounded-off
approximations thereof, unless otherwise specified. Moreover, while this
invention has been shown and described with references to particular
embodiments thereof, those skilled in the art will understand that
various substitutions and alterations in form and details may be made
therein without departing from the scope of the invention. Further still,
other aspects, functions and advantages are also within the scope of the
invention; and all embodiments of the invention need not necessarily
achieve all of the advantages or possess all of the characteristics
described above. Additionally, steps, elements and features discussed
herein in connection with one embodiment can likewise be used in
conjunction with other embodiments. The contents of references, including
reference texts, journal articles, patents, patent applications, etc.,
cited throughout the text are hereby incorporated by reference in their
entirety; and appropriate components, steps, and characterizations from
these references optionally may or may not be included in embodiments of
this invention. Still further, the components and steps identified in the
Background section are integral to this disclosure and can be used in
conjunction with or substituted for components and steps described
elsewhere in the disclosure within the scope of the invention. In method
claims, where stages are recited in a particular order--with or without
sequenced prefacing characters added for ease of reference--the stages
are not to be interpreted as being temporally limited to the order in
which they are recited unless otherwise specified or implied by the terms
and phrasing.